*Our Mathematical Universe*is a book by MIT physicist Max Tegmark. But a more appropriate title would be

*My Fantasies About Other Universes*. Tegmark has long been a popularizer of the idea that our universe is only one of a huge or infinite set of universes called a multiverse. Tegmark distinguishes between 4 types of multiverses, which he calls Level I, Level II, Level III, and Level IV. Tegmark says he is a believer in a Level IV multiverse. He describes a Level IV multiverse as one consisting of a vast or infinite number of universes, each of which has a different mathematical structure. This is not science, but unverifiable metaphysics dressed up in scientific garb.

Tegmark
gives some reasoning to support his belief in a Level IV multiverse,
but it is not persuasive. He claims that a belief in a Level IV
multiverse follows from the “mathematical universe hypothesis,”
which he defines as the idea that “our external physical reality is
a mathematical structure.” He defines a mathematical structure as
“a set of abstract entities with relations between them.”

But
this mathematical universe hypothesis is not a sound one. The
universe is not a mathematical structure, because it is not a set of
abstract entities. A mind can create various abstract entities when
pondering the universe, but such abstract entities are not the same
as the universe itself.

Consider
a much simpler question: is our planet a mathematical structure? No,
it is not. Our planet has the shape of a sphere, which is a
mathematical structure. But our planet is vastly more than just a
sphere, as a description of our planet would involve a vast number of
details beyond that of a sphere. Just as it incorrect to say that our
planet is a mathematical structure, it is incorrect to say that the
universe itself is a mathematical structure.

Tegmark
attempts to prove his mathematical universe hypothesis by arguing
that it follows from an “external reality hypothesis,” which he
defines as the hypothesis that there exists an external physical
reality completely independent of us humans. But such a mathematical
universe hypothesis in no way follows from such an external reality
hypothesis, and Tegmark's reasoning that the one follows from the
other is not at all convincing.

Tegmark
gives an example of a chess match in an attempt to persuade us that
everything can be reduced to a mathematical structure. He points out
that we can reduce the chess match to an abstraction listing each
piece and how it moved. But even this example fails. Even a chess
match cannot be reduced to an abstract mathematical structure. To get
the full story on what went on in a chess match, we must have not
just the movement of the pieces, but the mind stream of the players:
what exactly they were thinking at each point in the game, and what
exactly they were feeling. There is no way to represent such streams
of thought and feeling through an abstract mathematical
representation. Even if one considers only physical things, you then have to consider that according to Heisenberg's uncertainty principle, all subatomic particles have a quantum fuzziness, meaning that they cannot be defined exactly in terms of both movement and position, unlike chess pieces on a chess board. You cannot even make a precise exact mathematical description of the arrangement of all the particles in your body.

Being
something composed of almost infinitely diverse forms of matter that
are widely separated, and also streams of experience and
consciousness that cannot be mathematically represented, there is no
mathematical structure that corresponds to the universe. Saying as
Tegmark does that the universe is a mathematical structure is to make
the same kind of mistake as saying that an office building is a
blueprint or saying that an automobile is a 3D CAD model (or saying
that a C++ object is a C++ class).

Tegmark
has introduced the idea of the universe as a mathematical structure
so that he can use the idea as a kind of a springboard to a
multiverse theory. The idea has long been held that every type of
mathematical structure exists in some eternal Platonic sense. For
example, it has been held that there has eternally existed the idea
of a triangle, the idea of a square, and so forth, going up to a
figure with a countless number of sides. So Tegmark basically reasons
that if our universe is a mathematical structure, and if every
mathematical structure is real, then there must exist every
imaginable universe that corresponds to each of the different
possible mathematical structures. But this reasoning fails to
persuade, simply because Tegmark fails to establish the unwarranted
idea that our universe is a mathematical structure, an idea which has
not received appreciable support from previous thinkers.

One
can only ask: why does Max Tegmark have such an enthusiasm for
multiverse theory? I think I have a possible explanation. Perhaps
Tegmark wants to believe in many other universes because he thinks
that our universe is very boring.

Why
do I suggest that Tegmark thinks our universe is boring? Part of the
reason is given in the last chapter of Tegmark's book. Tegmark argues
that we are alone in our vast universe. He gives the same lame
argument that has been advanced by Ray Kurzweil and others, the argument
that if there were intelligent life elsewhere it would already have
colonized our solar system. This argument has been rebutted
successfully many times before, including in this post and this post. One reason
the argument makes no sense is that intergalactic travel
(involving distances of many thousands of light-years) is very probably impossible, and even interstellar travel is very probably
extremely difficult (contrary to impressions given by science fiction
such as

*Star Trek*and*Star Wars*). Another reason the argument makes no sense is that there is no large nation on Earth which develops more than 95% of available territory (every large nation keeps a significant fraction of its available territory as undeveloped preserves or nature reserves). So there is no reason to assume that any race would go around colonizing every available planet or solar system.
The
fact that we have found so many potentially habitable planets already
contradicts Tegmark's thesis that we are alone in the universe, as
does the fact that we live in a universe with at least
10,000,000,000,000,000,000 stars like the sun.

*Credit: Planetary Habitability Laboratory, UPR Arecibo*

Believing
unwisely in the idea that man is the only intelligent species in the
universe, Tegmark therefore believes in a dull desert of a universe,
a universe with no beings more interesting than those we read about
in our daily news. So we can
make a guess as to
why he is so attracted to speculations about other
universes. It's rather like this. Imagine if you had only one
sibling, a brother who was a real snooze, as dull as dishwater. You
might be tempted to fantasize that you are adopted, and that you have
unseen brothers you have never met, who live terribly exciting lives.
But if your brother was an extremely interesting person with a
fascinating life, you probably would not engage in such fantasies.

I
think we live in a universe vastly more interesting than the very dull
affair imagined by Tegmark. Contrary to what Tegmark claims, the
evidence from astronomy actually suggests that the universe is
teeming with intelligent life. We have every reason to suspect that
the history of our universe is the most fascinating drama imaginable,
a place where epics of evolution are being played out on trillions of
civilized planets existing in billions of galaxies. We also have much
evidence to suggest that the universe has a wide variety of
fascinating paranormal phenomena which make it far more interesting
than any materialist thinker can imagine.

How
would you concisely describe such a universe, with such a staggering
wealth of locations and phenomena, with such an incredible diversity
of intelligent entities, some of which are protoplasmic, some of
which may be electronic, and some of which may be purely spiritual?
You might call it the most interesting universe imaginable. When you
have that type of universe to study and ponder and investigate, why
even bother with unverifiable speculations about other universes?